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What is the sum of the numbers '12' and '21' in base-3?

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Question: What is the sum of the numbers \'12\' and \'21\' in base-3?

Options:

  1. 100
  2. 110
  3. 120
  4. 200

Correct Answer: 100

Solution: 

\'12\' in base-3 is 3 and \'21\' is 7. Their sum is 10, which is \'100\' in base-3.

What is the sum of the numbers '12' and '21' in base-3?

Practice Questions

Q1
What is the sum of the numbers '12' and '21' in base-3?
  1. 100
  2. 110
  3. 120
  4. 200

Questions & Step-by-Step Solutions

What is the sum of the numbers '12' and '21' in base-3?
  • Step 1: Understand that '12' in base-3 means 1*3^1 + 2*3^0.
  • Step 2: Calculate '12' in base-3: 1*3 + 2*1 = 3 + 2 = 5.
  • Step 3: Understand that '21' in base-3 means 2*3^1 + 1*3^0.
  • Step 4: Calculate '21' in base-3: 2*3 + 1*1 = 6 + 1 = 7.
  • Step 5: Add the two results: 5 + 7 = 12.
  • Step 6: Convert the sum (12) back to base-3.
  • Step 7: To convert 12 to base-3, divide by 3: 12 ÷ 3 = 4 (remainder 0).
  • Step 8: Divide 4 by 3: 4 ÷ 3 = 1 (remainder 1).
  • Step 9: Divide 1 by 3: 1 ÷ 3 = 0 (remainder 1).
  • Step 10: Read the remainders from bottom to top: 110 in base-3.
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